Distributed SUSY breaking: dark energy, Newton’s law and the LHC

Abstract

Abstract:We identify the underlying symmetry mechanism that suppresses the lowenergy effective 4D cosmological constant within some 6D supergravity models, generically leading to results suppressed by powers of the KK scale, m 2 KK , relative to the much larger size, m 4 , associated with mass-m particles localized in these models on codimension-2 branes. These models are examples for which the local conditions for unbroken supersymmetry can be satisfied locally everywhere within the extra dimensions, but are obstructed only by global conditions like flux quantization or by the mutual inconsistency of the boundary conditions required at the various branes. Consequently quantities (like vacuum energies) forbidden by supersymmetry cannot become nonzero until wavelengths of order the KK scale are integrated out, since only such long wavelength modes can see the entire space and so 'know' that supersymmetry has broken. We verify these arguments by extending earlier rugby-ball calculations of one-loop vacuum energies within these models to more general pairs of branes within two warped extra dimensions. JHEP07 (2014)034 numerical purposes we take m to be the top-quark mass and take M g as small as possible, consistent with energy-loss bounds from supernovae.) C is a constant depending on the details of the bulk spectrum, which could easily be of order 500 for each of hundreds of fields in the bulk. The value C ∼ 6 × 10 6 would give the observed Dark Energy density.

EFT for vortices with dilaton-dependent localized flux

“…Our goal is to understand how bulk properties (such as curvatures) are related to the asymptotic behaviour of the fields near any localized sources. Since this section on the bulk duplicates standard results [15,[21][22][23][32][33][34], aficionados in a hurry should skip it and go directly to the next section.…”

“…Such a relation between the defect angle and flux is also expected from the supersymmetry conditions, in order to guarantee the continued cancellation of spin and gauge connections within the Killing spinor's covariant derivative, once localized sources are introduced [11,12,34]. However, past works did not properly identify the defect angle with the renormalized brane tension, as in (5.13).…”

“…It is useful to see how the above general arguments go through for explicit solutions to the bulk field equations, which are known in great detail [32][33][34] when φ → 0 in the nearsource limit in the special case where d = 4 and D = 6 and V 0 = 2g 2 R /κ 4 . (See also [43][44][45][46][47] for a discussion of linearized solutions; [39,48,49] for solutions with 6 φ = 0; [56] with other fields nonzero; [48,[57][58][59][60] for time-dependent configurations; [61] with more than two brane sources; and with black hole solutions [62].…”

Self-tuning at large (distances): 4D description of runaway dilaton capture

“…From the point of view of the vacuum energy, the most dangerous renormalizations of the bulk are dimension-four interactions involving curvature squared terms (and their partners under supersymmetry) since these can acquire renormalizations proportional to the squared-mass, M 2 , of the massive bulk supermultiplet [51,[58][59][60][61]. These can generate contributions to the 4D vacuum energy of order M 2 / 2 , and so be larger than the 1/ 4 desired to describe Dark Energy in SLED models.…”

“…Loops within the supergravity describing the bulk have been studied in some detail [51,[58][59][60][61], and although loops of individual massive states do renormalize all terms in the bulk and brane lagrangians their contributions to the bulk lagrangian tend to cancel once summed over 6D supermultiplets [59][60][61]. The only bulk renormalizations that survive these cancelations are renormalizations of those interactions allowed by bulk supersymmetry, for which we do not make any special requirements.…”